From 1773 to 1777 Stein studied political economy, jurisprudence, and history at the university of Göttingen, where he made his first acquaintance with English institutions, his knowledge and appreciation of which are often manifest in his later career. His original intention was to qualify for an appointment in the imperial courts, but this sphere of work was little to his taste, and in 1780 he took the step, somewhat unusual for an imperial knight, of entering the service of Prussia. He became an official in the mining department, and by 1784 had risen to be head of the administration of mines and manufactures for Westphalia. In 1796 he was made supreme president of the provincial chambers of Westphalia, an appointment which gave him opportunity to evince his great administrative talents. In 1785 his administrative career was interrupted for a short time by a diplomatic mission to the elector of Mainz, and in 1786-87 he made a long professional tour in England, chiefly in the mining districts.

In 1804 Stein was created a minister of state, with the portfolio of excise, customs, manufactures, and trade. In this capacity he abolished the internal customs duties throughout Prussia, and effected several other needed reforms; but he was unable to modify the general disastrous tenour of the Prussian policy, which was now ripening for the catastrophe of Jena. Stein’s remonstrances with the king and his strictures upon the course of the administration were couched in the most open and unsparing language, and they were specially directed against the system of government through privy cabinet counsellors, who had practically come to supplant the ministers without possessing either an official knowledge of affairs or a ministerial responsibility. He refused to join in the reconstituted ministry after Jena unless this abuse were done away with, and Frederick William III., already wounded by the frankness of Stein’s criticism, sent him his dismissal in a most ungracious form (January 3, 1807). When the king, however, found himself left in the lurch by his ally Russia, at the peace of Tilsit (July 9, 1807), he turned in despair to the strong and candid counsellor he had dismissed half a year before, and invited Stein to re-enter his service, practically on his own terms. Curiously enough Stein’s appointment as minister president was encouraged by Napoleon, who seems to have seen in him merely the clever organizer and financier, who would most easily put Prussia in a position to pay the enormous war indemnity levied on it. Stein took office on October 4, 1807, and at once began that weighty series of organic reforms with which his name is most indissolubly connected. The emancipation edict appeared on October 9, 1807, a few days after the formal receipt of his powers, and the municipal ordinance was published on November 19, 1808. In the interim he co-operated zealously with Scharnhorst in the reconstitution of the army, carried out a number of important financial and administrative reforms, and prepared the way for a thorough reconstruction of the whole framework of government, which, however, he himself was not to have an opportunity to effect.

Stein’s momentous ministry did not last much more than a year. Napoleon soon awoke to the eminently patriotic and energetic character of the man he had incautiously recommended, and an intercepted letter gave him the opportunity to demand Stein’s dismissal. Frederick William had no option but to comply, as he shrank from the only possible alternative of an open breach with the French emperor. Stein was proscribed by Napoleon, his property in Westphalia was confiscated, and he himself had to take refuge in Austria from the French troops.

In 1812 the czar Alexander invited Stein to St Petersburg, where he filled the post of unofficial adviser to his imperial majesty on German or rather on anti-Napoleonic affairs; and it would perhaps be difficult to overestimate the influence of the proximity of such a man in keeping Alexander’s courage screwed to the sticking-point. When the scene of the campaign of 1812 was transferred to Germany, Stein was entrusted with the administration of the Prussian districts occupied by the Russian troops, and he shares with Yorck the merit of arousing East Prussia to take arms against the French, and so of calling the “Landwehr” into existence for the first time. To Stein also mainly belongs the credit of effecting that union of Russia and Prussia (treaty of Kalisch, February 27, 1813) which was perhaps the main factor in the overthrow of Napoleon. After the battle of Leipsic Stein became supreme president of a central commission appointed to administer the lands occupied by the allied armies, in which post he was indefatigable in providing the men and material necessary for a successful prosecution of the war. When the military struggle was over Stein’s work was practically done. The two tendencies of absolutism on the one hand and particularism on the other which determined the tone of the Vienna congress were equally repugnant to him, and he took little part in its deliberations. He also refused the invitations of Austria and Prussia to represent them at the Frankfort diet, a makeshift in which he had no confidence or hope. The rest of his life he spent in retirement, sharing his time between Frankfort and his property in Westphalia, and the only office he ever again filled was that of marshal of the provincial estates. In 1819 he founded the society for the publication of the Monumenta Germanise Historica, which has since done such admirable work. He died on June 29, 1831, in his seventy-fourth year, on his estate of Cappenberg in Westphalia, leaving a family of three daughters. His wife was Countess von Walmoden-Gim-born of Hanover, a granddaughter of George II.

Stein’s distinguishing merit as a statesman is that he was practically the first to see the urgent necessity of German unity, to contemplate its realization as possible, and to inaugurate a policy likely to bring it about. That which, now that it has been accomplished by Stein’s great successor, seems to us almost a matter of course, was a mere chimera to most of our forefathers, and it required the faculty of a political seer to attain Stein’s clear views of future possibilities. Stein saw, too, that the only hope of salvation lay in the people as such,—that he must enlist the sympathies of the nation and raise its moral tone. To this end a series of great and just reforms was necessary. If a deep national sentiment was to be evoked, the people must be freed from feudal burdens; if they were to carry on an effective struggle for independence, they must first acquire personal liberty. His emancipation edict, therefore, which has been called the habeas corpus act of Prussia, abolished serfdom, did away with the distinctions of caste, and abrogated the feudal restrictions upon the free disposition of person and property (compare Prussia, vol. xx. pp. 11, 12). This reform, however, Stein found, in a sense, ready to his hand; it was demanded by the spirit of the times, and can hardly be looked on as a purely individual achievement. His most distinctive work was a great scheme of political reform, in which he contemplated the conversion of the absolute monarchy of Prussia into a free representative state. He wisely began the process by introducing the principle of free local government in his Stadte-Ordnung, or municipal ordinance. The people had to be roused to take an interest in governing themselves, and it was easier to expand this interest from the local to the national than to work down from the national to the local. Stein did not see much more than this beginning of his plans, but the famous “Political Testament” he drew up on leaving office show's how wide-sweeping were the reforms he contemplated. The right of self-government was to be extended to the rural communes, and a thorough reform of every branch of the administration was to be effected, while the coping-stone of the new edifice was to take the form of a free representative parliament. Time, however, has been on his side, and it is not too much to say with Prof. Von Treitschke that every advance Germany has since made in political life has brought it nearer the ideals of Stein.

The standard work on Stein is the biography by G. H. Pertz, G vols., 1849-55, but few English readers will feel the need of going beyond Prof. Seeley’s admirable Life and Times of Stein, London, 1879, which also contains a full bibliography.

In his Systematische Entwickelung der Abhängigkeit geometrischer Gestalten von einander he laid the foundation on which synthetic geometry in its present form rests. He introduces what are now called the geometrical forms (the row, flat pencil, &c.), and establishes between their elements a one-one correspondence, or, as he calls it, makes them projective. He next gives by aid of these projective rows and pencils a new generation of conics and ruled quadric surfaces, “which leads quicker and more directly than former methods into the inner nature of conics and reveals to us the organic connexion of their innumerable properties and mysteries. In this work also, of which unfortunately only one volume appeared instead of the projected five, we see for the first time the principle of duality introduced from the very beginning as an immediate outflow of the most fundamental properties of the plane, the line, and the point, so that a proof of its correctness is not required.

In a second little volume, Die geometrischen Constructionen ausgeführt mittelst der geraden Linie und eines festen Kreises (1833), he shows, what had been already suggested by Poncelet, how all problems of the second order can be solved by aid of the straight-edge alone without the use of compasses, as soon as one circle is given on the drawing paper.

The rest of Steiner’s writings are found in numerous papers mostly published in Crelle's Journal, the first volume of which contains his first four papers. The most important are those relating to algebraical curves and surfaces, especially the short paper Allgemeine Eigenschaften algebraischer Curvem This contains only results, and there is no indication of the method by which they were obtained, so that, according to Hesse, “they are, like Fermat’s theorems, riddles to the present and future generations.” Eminent analysts succeeded in proving some of the theorems, but it was reserved to Cremona to prove them all, and that by a uniform synthetic method, in his book on algebraical curves. Other important investigations relate to maxima and minima. Starting from simple elementary propositions, Steiner advances to the solution of problems which analytically require the calculus of variation, but which at the time altogether surpassed the powers of that calculus. Connected with this is the paper Vom Krümmingsschwerpuncte ebener Curven, which contains numerous properties of pedals and roulettes, especially of their areas.

Steiner’s papers have been collected and published in two volumes by the Berlin Academy. His lectures on synthetic geometry, containing the theory of conics, have been published since his death, edited by Geiser and Schröter. Biographical notices are contained in Geiser’s pamphlet Zur Erinnerung an J. Steiner (Schaffhausen, 1874).